Question

An investor wants to invest his money in a fund which has maintained a steady value. A fund manager claims that one of his bond funds has maintained an average price of $7.00$⁢7.00 with a variance of 0.180.18. In order to find out if the fund manager's claim is true, the investor samples the prices from 2121 random days and finds a standard deviation of 0.25530.2553 in the price. Can the investor conclude that the variance of the share price of the bond fund is less than claimed at α=0.025α=0.025? Assume the population is normally distributed.

Step 1 of 5:

State the null and alternative hypotheses. Round to four decimal places when necessary.

Step 2 of 5:

Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Step 3 of 5:

Determine the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5:

Make the decision.

Step 5 of 5:

What is the conclusion?

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ^2 = 0.18
Alternative Hypothesis, Ha: σ^2 < 0.18

2)

Rejection Region
This is left tailed test, for α = 0.025 and df = 20
Critical value of Χ^2 is 9.591
Hence reject H0 if Χ^2 < 9.591

3)

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (21 - 1)*0.0652/0.18
Χ^2 = 7.244

4)

Reject the null hypothesis

5)

There is sufficient evidence to conclude that the variance of the share price of the bond fund is less than claimed at α=0.025